# Question #1b9b0

##### 3 Answers

Find

Find when

Increasing on

hmmmmm

The graphing function for Socratic is currently not responding. I have done as much as I can without it. I leave the answer to you to work out the rest of, and will update this once the system is back in order.

#### Explanation:

#f(x)=sin(2x)/x#

Through the quotient rule,

#f'(x)=(2xcos(2x)-sin(2x))/x^2#

When

graph{(2xcos(2x)-sin(2x))/x^2 [-0.1, 6.3, -4.2, 5.8]}

To find when

#f''(x)=-((4x^2-2)sin(2x)+4xcos(2x))/x^3#

Graphing this to identify when it is negative, which corresponds to when

graph{-((4x^2-2)sin(2x)+4xcos(2x))/x^3 [-0.1, 6.3, -48.1, 49.8]}

See explanation and graph.

#### Explanation:

graph{y-(sin (2x))/x=0 [-10, 10, -5, 5]}

sin 2x takes alternate signs in

The zeros of the function are at

The concavity is up and down, alternately, at points of inflexion,

where the tangent crosses the curve. Seemingly, they are in

between zeros of f..

For precise locations, look for zeros of f''=o, by numerical iterative

methods. If I get these zeros, I would add them here in the next

edition. The graph easily reveals these tangent-crossing-curve

locations. But it lacks precision

he inserted Mountain-Hills range in the graph provides visual

effect. Nature is also a synonym to Mathematics that provide models

to natural phenomena.